Preheat your oven to 375°F (190°C).
Place the diced eggplant in a colander, sprinkle with a teaspoon of salt, and let sit for 20 minutes. This draws out bitter flavors. Rinse and pat dry with paper towels.
Heat 2 tablespoons olive oil in a large oven-safe skillet or Dutch oven over medium-high heat. Add the eggplant and cook until lightly browned, about 5-7 minutes. Remove and set aside.
In the same pan, add the remaining tablespoon of oil. Add onions and cook until translucent, about 4 minutes.
Add the garlic and cook for 30 seconds until fragrant.
Add zucchini and bell peppers. Cook for 5-7 minutes until they begin to soften.
Stir in the diced tomatoes, tomato paste, thyme, rosemary, bay leaf, and the cooked eggplant.
Season with salt and pepper to taste. Bring to a simmer.
Cover and transfer to the oven. Bake for 30 minutes until vegetables are tender but not mushy.
Remove from oven, discard the bay leaf, and stir in the balsamic vinegar and fresh basil.
Let rest for 10 minutes before serving. The flavors will continue to develop as it sits.